Editing Salem number (section)

== Properties ==

Because it has a root of absolute value 1, the [[minimal polynomial (field theory)|minimal polynomial]] for a Salem number must be a [[reciprocal polynomial]]. This implies that <math>1/\alpha</math> is also a root, and that all other roots have absolute value exactly one. As a consequence α must be a [[unit (ring theory)|unit]] in the [[ring (mathematics)|ring]] of algebraic integers, being of [[field norm|norm]] 1.

Every Salem number is a [[Perron number]] (a real algebraic number greater than one all of whose conjugates have smaller absolute value).